8s+6d=420
3D= s
8s+6(s/3)=420
10s=420
s= 42
dragonflies altogether have 420 legs, number of spiders are 3 times the
number of dragonflies, the number of spiders are?
3D= s
8s+6(s/3)=420
10s=420
s= 42
Let's say the number of spiders is S and the number of dragonflies is D.
Given that a spider has 8 legs and a dragonfly has 6 legs, we can write an equation for the total number of legs:
8S + 6D = 420 (Equation 1)
Given that the number of spiders is 3 times the number of dragonflies, we can write another equation:
S = 3D (Equation 2)
Now we can solve this system of equations to find the values of S and D.
Substitute the value of S from Equation 2 into Equation 1:
8(3D) + 6D = 420
24D + 6D = 420
30D = 420
Divide both sides of the equation by 30:
D = 420/30
D = 14
Now substitute the value of D into Equation 2 to find S:
S = 3(14)
S = 42
So, the number of spiders is 42.
Let's denote the number of spiders as "x" and the number of dragonflies as "y".
According to the given information:
- A spider has 8 legs, so the total number of spider legs would be 8 times the number of spiders: 8x.
- A dragonfly has 6 legs, so the total number of dragonfly legs would be 6 times the number of dragonflies: 6y.
We are also given that the total number of legs from spiders and dragonflies combined is 420 legs. So, we can set up the equation:
8x + 6y = 420
Additionally, the number of spiders is mentioned to be 3 times the number of dragonflies:
x = 3y
Now that we have two equations, we can solve them simultaneously to find the values of x and y.
Using the second equation, we can substitute x in terms of y into the first equation:
8(3y) + 6y = 420
24y + 6y = 420
30y = 420
y = 420 / 30
y = 14
Now, we can substitute the value of y back into the second equation to find x:
x = 3y
x = 3 * 14
x = 42
Therefore, the number of spiders is 42.